A242180 Least prime divisor of q(n) which does not divide any q(k) with k < n, or 1 if such a primitive prime divisor does not exist, where q(.) is the strict partition function given by A000009.

1, 1, 2, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 11, 1, 1, 19, 23, 1, 1, 1, 89, 13, 61, 71, 1, 1, 37, 1, 1, 17, 1, 7, 1, 1, 167, 1, 1, 491, 53, 1, 31, 1, 227, 1, 1, 1, 97, 1, 59, 241, 29, 1, 953, 1063, 1777, 1, 367, 1, 1

Offset: 1

Author

Zhi-Wei Sun, May 06 2014

Keywords

• nonn

Comments

Conjecture: a(n) > 1 for all n > 203.

Examples

			a(8) = 1 since q(8) = 2*3 with 2 = q(3) and 3 = q(5).
a(23) = 13 since q(23) = 2^3*13 with 13 not dividing q(1)*q(2)*...*q(22), but 2 divides q(3) = 2.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..6000

Crossrefs

Cf. A000009, A000040, A084911, A194261, A272170, A272171, A272173.

Programs

Mathematica

f[n_]:=FactorInteger[PartitionsQ[n]]
pp[n_]:=Table[Part[Part[f[n],k],1],{k,1,Length[f[n]]}]
Do[If[PartitionsQ[n]<2,Goto[cc]];Do[Do[If[Mod[PartitionsQ[i],Part[pp[n],k]]==0,Goto[aa]],{i,1,n-1}];Print[n," ",Part[pp[n],k]];Goto[bb];Label[aa];Continue,{k,1,Length[pp[n]]}];Label[cc];Print[n," ",1];Label[bb];Continue,{n,1,60}]